5 Second order linear regression Trust Flow vs. Domain Authority

Majestic Trust Flow or Moz Domain Authority for SEO?

Reports Comments (9)

In Search Engine Optimisation (SEO), you often want to know how strong a website is. Two different metrics that attempt to measure this are Domain Authority (DA) from Moz and Trust Flow (TF) from Majestic

Both Trust flow and Domain Authority help SEO professionals make judgements about the usefulness of backlinks from a site in order to ensure their website ranks higher in Google (and other search engines).

What I’ve been wondering is: do they measure the same thing? That’s what we will find out in this report.


If the two metrics measure the same thing (they correlate), it would suggest two things:

First, you can translate one into other. This can be useful in practice when for example when you want to compare sites but don’t have all the data.

Second, if two metrics correlate, this suggests the are probably both pretty good metrics . Because what are the odds that two companies independently both get it wrong in the same way?

However, if the metrics are not similar (when there is little correlation between them), it would seem that at least one of them must must be wrong.

Last year, we already concluded that Trust Flow is a good predictor of organic search engine traffic to a domain. This is an indication that is is a good metric for estimating the strength of a domain  from a search engine perspective.


To analyse the similarity  I first collected the Domain Authority and Trust flow for a sample of 2309 domains. The sample was created from domains that that rank on Google.co.uk for keywords related to celebrity gossip and showbiz news. 

Note that the topic of the domains is not relevant to the conclusion of the study. It is expected generalise to all websites, regardless of their category.

To analyse the data, I used linear regression. This statistical method enables me to estimate the relationship between Domain Authority and Trust Flow. It also lets me determine correlation bewteen the metrics, which is a meassure of the strength of this relationship.

The Data

Before we start, I want to get to know the data a bit better. Below are two charts, one for Trust Flow and one for Domain Authority, that shows the 2309 domains and how they are distributed over the values of the respective metrics. Each x axis is divided it bars of 10. On the Y axis is the count of domains in that group.

We can see that metrics have more low quality than high quality domains. However where Majestic has most of its sites under Trust Flow 30. Domain authority has most between 10 and 40.

Trust flow’s higher value domains gradually reduce in quantity as the Trust Flow increases. Domain Counts for Domain Authority’s higher values stay constant up to DA 100.


1 Majestic histogram 2 Moz histogram


Regression analysis

We want to understand how Trust Flow and Domain Authority are related, and how strong the relationship is. Both goals are achieved through regression analysis. This means that we let the computer draw the best fitting line through the points in the charts below. How well this line fits the points determines the strength of the relationship (correlation). This can be expressed as the correlation coefficient R^{2}.

Regression 1

In the chart below, every black dot represents one of the 2309 domains analysed, with their Trust Flow value on the Y axis, and Domain Authority on the X axis. The thin blue line is the average Trust Flow at the corresponding level of Domain Authority. The red line is the best fit for the first order relationship between Trust Flow and Domain Authority. A first order relationship means that it is a formula in the form:

y = a + bx


Were a and b are the coefficients to be found by the regression analysis. 

3 First order linear regression Trust Flow vs. Domain Authority


The analysis shows that the relationship between TF and DA is:

TF = -7.92 + 0.78 * DA


The correlation for this formula is:

R^{2} = 0.8023


This is a very high number that suggests that Trust Flow and Domain Authority can are related. Specifically, more than 80% of the value of Trust Flow can be explained when you know the Domain Authority of a website and the other way round.


Residuals 1

We can learn more about the relationship between TF and DA by analysis the residuals of the regression model. The residuals are the difference between the real values, and the values predicted by the formula calculated in the regression analysis. The residuals (difference) of Trust Flow are plotted on the y axis against the predicted  Trust Flow on the x axis. The blue line is the smoothed average at the corresponding Trust Flow value

.4 First order linear regression Residials vs. Predicted Trust Flow



In a well-fitting model the residuals are equally distributed above and below the y = 0 line for all values of the x axis. In this chart that is mostly true. However, in the low and high values of the prediction, the line goes up. This means it that appears the model underestimates the actual Trust Flow when we know the Domain Authority. Maybe the model can be improved.

Regression 2

When we look at the first scatter plot, it seems that the dots follow a slightly curved trajectory. Therefore it may be appropriate to try a second order polynomial regression. This means we try to find a formula in the form:

y = a + bx + cx^{2}


The plot below shows the same dots as in the first chart, but now the red line represents this second order relationship.5 Second order linear regression Trust Flow vs. Domain Authority


In this case, the relationship can be expressed as follows:

TF = 3.134 + 0.215 * DA+ 0.054 * DA^{2}


The correlation for this formula is

R^{2} = 0.826


The correlation for this formula is slightly higher than the first order equation. Thus, this formula is better than the previous. We can also see this in the residuals plot below.

Residuals 2

6 Second order linear regression Residials vs. Predicted Trust Flow


This plot shows that in the lower levels of predicted Trust Flow, the relation is much better. In the higher values it’s still skewed upwards, though less than in the first order relationship.

Confidence intervals

Thus as analysed above, it appears that we can use the formula

TF = 3.134 + 0.215 * DA+ 0.054 * DA^{2}


To calculate Trust Flow from Domain Authority. A correlation of over 82% means that it is mostly correct, but as the residuals chart shows, in many cases the actual value is higher or lower than the predicted one. To get a better understanding of the relationship, we can calculate a confidence interval where 95% of the time, the actual Trust Flow value will fall inside.

The formulas for the upper and lower limits of the confidence intervals are as follows:



In this post I showed how we can translate the Moz Domain Authority into MajesticSEO Trust Flow. The relationship has a correlation coefficient   R^{2} of 0.82. This suggests that the two metrics are mostly measuring the same thing, and can thus be substituted for each other. We use the quadratic equation to map the DA to TF.

Because there is a spread in the results, it may be better to express the relationship as confidence intervals. The formulas for the 95% confidence interval have specified.

The practical meaning of this analysis has been to show that MajesticSEO and Moz mostly agree on their way of classifying authority of website. Moz is more generous than Majestic giving higher values, but this in itself doesn’t tell you which metric is better.

That’s because this analysis cannot tell us which of the metrics are more closely related to SEO performance. It does however instil confidence because two companies independently create proxies for PageRank that agree with each other. Hopefully this means they also agree with Google.


For your convenience, I provided below a table that you can use to translate a Domain Authority of a site into the corresponding Trust Flow, and vice versa. The 95% confidence interval column gives the amount that you need to add or subtract to stay within the interval. Note that all values are rounded to the nearest integer. For example, a Domain Authority of 10 is 95% of the times equal to Trust Flow between 8 and 12.

Domain authorityTrustflowTrustflow 95% confidence (up or down)
Article Name
Majestic Trust Flow or Moz Domain Authority for SEO?
How well do Moz Domain Authority and MajesticSEO Trustflow correlate? This article applies regression analysis to describe the relationship between them, so that you can convert one into the other.
Pin It

» Reports » Majestic Trust Flow or Moz...
On February 24, 2014
, , , , , , ,

9 Responses to Majestic Trust Flow or Moz Domain Authority for SEO?

  1. Gillis,
    Thankyou for your work. I understand that Majestic & MOZ have their different metrics. It would be nice if we could have a single metric. Thanks for your attempt to bring some correlation between them. The SEO community definitely needs this. Nice report.

  2. […] Then its important to order the links by some sort of solid metric. My favourite is Majestic Trust Flow because it correlates really well with actual visibility on Google search results. The logic being ‘if google loves a site, then links from that site will have value’. We did some analysis on this correlation here: LINK and if you have a thing for Moz domain authority as a metric, then have a look at this correlation analysis here: LINK […]

  3. Khushal says:

    This is getting a little tough to understand. I am trying to report our link building activity and stuck between choosing Domain Authority or Moz Trust flow as a quality of link metric. What do most SEO’s recommend?

  4. matt says:

    Thanks for the table…It helped me a lot. With the sea of data majestic provides, all I need to do now is figure out which is most important.

    Great report!

    • admin says:

      I don’t have a very much confidence in moz domain authority data, and the other issue is that all link analysis data is being weakened by disavow, so to get the real answer you will probably have to cross reference against sem rush data which will then tell you weather a site ranks or not.

  5. […] initial quick check? Most important re authority and trust of a domain are Moz DA and Majestic TF (comparing those two), while Majestic TF has the advantage that it is based on quality check of human SEO experts that […]

  6. Igor Mateski says:

    Thank you for the solid report. It was a great read. I’m using a Majestic CSV for a backlinks analysis and wanted to find out how trust flow is generated.
    Im working with roughly 50.000 backlinks that point to various places on a site with about 2000 pages. Since the previous on-site analysis of the Flesch-Kincard Grade Level and traffic to individual pages didn’t return any solid conclusions (no correlation between text quality and traffic amount), I now am trying to figure out if I can make a direct relationship between traffic and number of backlinks (and then another iteration with backlinks that have some TF).
    It’s going to be an interesting study.

    • admin says:

      That sounds like a really interesting piece of analysis. I’ve been looking at a lot of high level correlation data as well recently. The angle i’m coming out is around trust and links For instance sites that are trusted and which have good length will rank well.

      We have clients who have terribly badly optimised sites but who rank across the board for some very competitive phrases. For that reason i’m not really focusing on things like text quality…I’m more interested in things like signals from third parties and manual reviewers.

  7. Thank you for the awesome analysis you’ve posted here. Looks like it was a lot of work, and it’s nice knowing there’s a fairly strong correlation between MOZ DA and Majestic SEO’s Trustflow. I just checked and my site has a DA of 21 and Trustflow of 8. My DA has recently dropped a couple of points from 23.

    I may be guilty of over checking stats when I should be focusing on creating good content. But I love numbers and stats!

    Keep us the great work!

Leave a Reply

Your email address will not be published. Required fields are marked *

You may use these HTML tags and attributes: <a href="" title=""> <abbr title=""> <acronym title=""> <b> <blockquote cite=""> <cite> <code> <del datetime=""> <em> <i> <q cite=""> <strike> <strong>

« »